What is the integral of arcsin(sqrt(x/(x+1))) ?

The integral of arcsin(sqrt(x/(x+1))) is xarcsin(sqrt(x/(x+1)))+arctan(sqrt(x))-sqrt(x)+C

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integral of arcsin(sqrt(x/(x+1)))

\int arcsin (\frac{x}{x + 1}) d x

x arcsin (\frac{x}{x + 1}) + arctan (x) - x + C

Solution steps

\int arcsin (\frac{x}{x + 1}) d x

Apply Integration By Parts

: x arcsin (\frac{x}{x + 1}) - \int \frac{x}{2 ( x + 1 )} d x

= x arcsin (\frac{x}{x + 1}) - \int \frac{x}{2 ( x + 1 )} d x

\int \frac{x}{2 ( x + 1 )} d x = - arctan (x) + x

= x arcsin (\frac{x}{x + 1}) - (- arctan (x) + x)

Simplify

= x arcsin (\frac{x}{x + 1}) + arctan (x) - x

Add a constant to the solution

= x arcsin (\frac{x}{x + 1}) + arctan (x) - x + C

\frac{\partial}{\partial x} (e^{- \frac{1}{2} x y})

\int - 2 x + 6 d x

y^{^{'}} + \frac{1}{x + 7} y = x^{- 2}, y (1) = 4

\frac{\partial}{\partial x} (x cos (x) cos (y))

What is the integral of arcsin(sqrt(x/(x+1))) ?
The integral of arcsin(sqrt(x/(x+1))) is xarcsin(sqrt(x/(x+1)))+arctan(sqrt(x))-sqrt(x)+C